Thomas Jefferson wrote about separation of religion (church) and state in 1802.
The First Amendments of the US Bill of Rights prohibits US Congress from making laws respecting an establishment of religion.
The Amish, the very conservative Christians in US, upholds this stand and forbid acceptance of government fund.

Religions should take care of themselves.
There must be no funding from government, enforcement of religious law by government or banning of religious speech.

Religions are not the same.
Even if there is one religion that is good, the precedence must not be set on letting the state have authority over religion.
This is because there are other religions that are hostile and authoritarian, and they can easily take over the current establishment by force.
When a hostile religion takes over, it can use government to execute their apostates or to coerce headcovering on women.
That government will also put the religion as a mandatory syllabus for everyone to study.
After all, government should just remain small and only focus on its fundamental roles.

In the separation process, existing flags that carry a religious symbol do not have to be changed because the flags also reflect the history of the nation.